Non-linear Kinetic Characteristics And Analysis For Chaos Motion Of The Shallow Reticulated Spherical Shell Under Compand Load

In this paper, nonlinear mechanics behavior of the shallow reticulated spherical shell is studied. The state of interior of country and overseas are introduced. Analysis and calculation of the shallow reticulated spherical shell in the aspect of static with dynamical and combined load are studied systematically. It provides the theory evidence to the application of the project. According to the nonlinear dynamical theory of plate and shell, modern analytic method of nonlinear dynamic is selected, and ideology of continuous quasi-shell method is used, reticulated shell is transformed into continuous shell, nonlinear dynamical governing equations are elected, boundary conditions and initial conditions are given. The nonlinear bending problem of shallow reticulated spherical shell, nonlinear natural frequency problem of the shallow spherical reticulated shell, dynamical stability problem of the shallow spherical reticulated shell, bifurcation problem and chaos problem of the shallow spherical reticulated shell are studied.At first, significance of the study on reticulated shells, bifurcation and chaoswere introduced. Then, domestic and foreign developing status of the study onreticulated shells was introduced.The nonlinear bending problem of shallow reticulated spherical shell was studied in chapter two. The equations of middle cross section of the three-dimensional reticulated frame and initial deflection are added to the equations of three-dimensional reticulated frame, then the equations of shallow spherical reticulated shell are obtained. Under the boundary conditions of fixed and clamped, the nonlinear bending problems of the shallow spherical reticulated shell objected to even load are solved by the method of modified iteration. The quadratic approximate analytic solution with the much higher accuracy is presented. The diagram of curves of loads and deflections with quadratic eigenvalue is superior to the diagram of first eigenvalue.The nonlinear natural frequency of the shallow spherical reticulated shell was solved in chapter three. According to nonlinear dynamical theory of shallow shell, nonlinear dynamical equations of the shallow spherical reticulated shell is obtained by the method of quasi-shell. The maximal amplitude in the center of the shallow spherical reticulated shell is selected as the perturbation parameter, and the problem is solved by perturbation variation. In its first approximate equations, linear natural frequency is obtained, in its second approximate equations, natural frequency of the shallow spherical reticulated shell is nonlinear obtained.The problem of the nonlinear dynamical stability of the shallow reticulated spherical shell under static combined load and load of both dynamic and static was analyzed. Due to nonlinear dynamical variation equations and compatible equations of the shallow reticulated conical shell, a nonlinear differential equation with quadric items was obtained by the Galerkin method under the fixed edges boundary condition. In order to discuss chaos motion, a kind of nonlinear dynamical free oscillation equation was solved. The problem of statistic at the equilibrium point of the system was discussed using exponent Floguet. Accurate solution to the free oscillation equation of the shallow reticulated spherical shell was obtained. Then Melnikov function was solved, critical conditions of chaos motion under different multiple were given and the existence of chaos motion was confirmed through the digital simulation phase plans and the PoincarémapNonlinear dynamical stability of this shallow spherical reticulated shell is analyzed by the method of catastrophe in chapter five. Based on the nonlinear dynamical theory of thin shells, according to the large deflection fundamental equations of the shallow reticulated spherical thin shells the nonlinear dynamical fundamental equations are established by using the modified iteration method to solve the secondary approximate analytical solution and look the large deflection solution as the initial deflection under the boundary conditions of clamped edges. Displacement model is given according to the boundary conditions of clamped edges and the tension is obtained by using displacement model. The equation of the balanced surface is obtained by using the first variation of the dynamic potential equaled zero. The system of equations and the sketch map of the corresponding bifurcation point set of the corresponding balanced surface are given.